It means the atom's electrons are less tightly held and more easier distorted by a near by charge.For example I- has 54 e- and its outer electrons are less tightly held than those of Cl- which has 18e-.

When it is polarizable it means that there are an equal amount of negative and positive charges of electrons within an object.Because there is a separation in the charge that means that there is not an imbalance in the charges.